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Introduction

Switch modeling

• produce both states of switch

• use model to optimize switch

Mass action modeling

Definition

• differential equations

• each equation is a sum of rates

• each rate is proportional to each of its reactants

Benefits of mass action modeling, i.e. why we used it

• form of mass action models/solvability doc

Analytical modeling

• benefits

   • naturally standardized
   
   • given parameters, it precisely predicts behavior

   • accurately predicts the data needed to determine parameters

   • allows avoidance of numerical errors like rounding

• ERSESCO

   • equation

   • reduction

   • solution

   • equilibration

   • stabilization

   • calibration

   • optimization

SimBiology

• numerical approximation

• diagram / schematic

Model of Recombinase Expression

Model of the Switch

The Switch Model describes how the switch equilibrates when the concentrations of the recombinases FimE and Hbif approach constant values. This model assumes that each recombinase catalyzes a one way reaction. This model predicts the degree of cooperativity n and m in the binding reaction of the recombinase to DNA for FimE and Hbif, respectively. Furthermore, this model predicts the forward catalysis rate constants, kF and KH, for FimE and Hbif.

Model of Inducible Hbif

The Inducible Hbif Model describes how the switch flips when acted upon by the Lux/HSL-controlled expression of Hbif. In this model, [HSL] represents the concentration of the species HSL:pLux:LuxR, the complex that promotes the expression of Hbif. In this model [HSL] is a function of pLux and LuxR expression levels in the cell, the amount of HSL added, and the fractional occupancies at the complexation equilibrium. It can be assumed that this complexation reaction happens instantaneously with respect to the slow, rate-limiting translation step of Hbif.

Expression Model

Equation:

Reduction: None

Solution:

Equilibration:

Stabilization:

Calibration:

Optimization:

SimBiology:

Expression Model Derivation

Switch Model

Equation:

Reduction:

Solution:

Equilibration:

Stabilization:

Calibration:

Optimization:

SimBiology:

Switch Model Derivation

Inducible Hbif Model

Equation:

Reduction:

Solution:

Equilibration:

Stabilization:

Calibration:

Optimization of Hbif:

Optimization of ON:

SimBiology:

Inducible Hbif Model Derivation

Future Directions

Data!